Charged Higgs Signatures at Future Electron-Proton Colliders

In this work, we present a detailed collider phenomenology study of the charged Higgs boson within a Beyond the Standard Model (BSM) framework featuring an extended gauge and scalar sector. The charged Higgs can decay via conventional modes, such as $H^- \to \bar{t}b$ and $H^- \to W^-h$, as well as through exotic channels like $H^- \to W'Z$ (or $WZ'$). These decays lead to distinct final-state topologies determined by the nature of the intermediate particles. We perform a comprehensive phenomenological analysis at future electron-proton colliders, namely the LHeC and FCC-eh, considering the luminosity projections provided in their design reports. Our results indicate that the conventional decay modes of the charged Higgs boson can achieve observable sensitivity and even discovery prospects at sufficiently high luminosities. In contrast, the exotic decay channel $H^- \to W'Z$ does not exhibit any viable discovery potential. These findings highlight the complementarity of future electron-proton colliders in probing extended Higgs sectors, particularly through conventional charged Higgs signatures.